sara travels twice as far as Eli when going to camp. Ashley travels as far as Sara and Eli together. Hazel travels 3 times as far as Sara. In total , all four travel a total of 888 miles to camp. How far do each of them travel?

Answers

Answer 1

Answer: Let's represent how far Eli travels as x.
Sara travels twice as far as that, so 2x.
Ashley travels as far as Eli and Sara combined. x + 2x = 3x.
Hazel travels 3× as far as Sara, and 3×2x = 6x.

All of these add up to 888.
x + 2x + 3x + 6x = 888
Let's add up these like terms.
12x = 888
We can then divide each side by 12...
x = 74

Therefore, Eli traveled 74 miles!
We can use this value to figure out everyone else's distances as well.
Sara = 2 × 74 = 148
Ashley = 3 × 74 = 222
Hazel = 6 × 74 = 444

Answer 2

Answer:

Sara: 148 miles
Eli: 74 miles
Ashley: 222 miles
Hazel: 444 miles

Further explanation

Given:

Sara travels twice as far as Eli when going to camp.
Ashley travels as far as Sara and Eli together.
Hazel travels three times as far as Sara.
In total, all four travel a total of 888 miles to camp.

Question:

How far does each of them travel?

The Process:

Notice of the four people, the easiest way is to start from Eli.

Let's call Eli's travel as x.

$\boxed{ \ Eli's \ travel = x \ }$

Sara travels twice as far as Eli.

$\boxed{ \ Sara's \ travel = 2x \ }$

Ashley travels as far as Sara and Eli together.

$\boxed{ \ Ashley's \ travel = x + 2x \rightarrow \boxed{ \ Ashley's \ travel = 3x \ }}$

Hazel travels three times as far as Sara.

$\boxed{ \ Hazel's \ travel = 3 * 2x \rightarrow \boxed{ \ Hazel's \ travel = 6x \ }}$

In total, all four travel a total of 888 miles to camp. Meaning, all of the above adds up to 888.

$\boxed{ \ x + 2x + 3x + 6x = 888 \ }$

$\boxed{ \ 12x = 888 \ }$

$\boxed{ \ 12 \cdot x = 888 \ }$

Both sides multiplied by 12.

$\boxed{ \ x = 888 / 12 \ }$

$\boxed{\boxed{ \ x = 74 \ }}$

We have obtained x. The final step is to substitute the value of x for each person's travel.

$\boxed{ \ Eli's \ travel = x \rightarrow \boxed{ \ Eli's \ travel = 74 \ miles \ }}$
$\boxed{ \ Sara's \ travel = 2x \rightarrow \boxed{ \ Sara's \ travel = 2 * 74 = 148 \ miles \ }}$
$\boxed{ \ Ashley's \ travel = 3x \rightarrow \boxed{ \ Ashley's \ travel = 3 * 74 = 222 \ miles \ }}$
$\boxed{ \ Hazel's \ travel = 6x \rightarrow \boxed{ \ Hazel's \ travel = 6 * 74 = 444 \ miles \ }}$

Thus we already know how far each of them travels.

- - - - - - -

The summary scheme is as follows:

Eli's travel ⇒ $\boxed{x}$
Sara's travel ⇒ $\boxed{x}\boxed{x}$
Ashley's travel ⇒ $\boxed{x}\boxed{x}\boxed{x}$
Hazel's travel ⇒ $\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}$

$\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x} = 888$

$\boxed{ \ 12 \cdot x = 888 \ }$

$\boxed{ \ x = 888 / 12 \ }$

Hence, the value of x is $\boxed{\boxed{ \ x = 74 \ }}$

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Keywords: Sara travels, twice, as far as, Eli, when going to camp, Ashley, Hazel, three times, In total, all four travel, 888 miles, how far, each, substitute

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